Towards chaos criterion in quantum field theory

Kuvshinov, V. A.; Kuzmin, A. V.

doi:10.1016/s0375-9601(02)00275-x

Cited by 13 publications

(23 citation statements)

References 12 publications

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“…Moreover it is known that classical gauge field theories are inherently chaotic [22]. Therefore the study of chaos assisted instanton tunneling in gauge field theories based on chaos criterion in quantum field theory [23] is also of essential interest.…”

Section: Resultsmentioning

confidence: 99%

Chaos-assisted instanton tunneling in one-dimensional perturbed periodic potential

Kuvshinov

Kuzmin²,

Shulyakovsky³

2003

Phys. Rev. E

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For the system with one-dimensional spatially periodic potential we demonstrate that small periodic in time perturbation results in appearance of chaotic instanton solutions. We estimate parameter of local instability, width of stochastic layer and correlator for perturbed instanton solutions. Application of the instanton technique enables to calculate the amplitude of the tunneling, the form of the spectrum and the lower bound for width of the ground quasi-energy zone.

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Section: Resultsmentioning

confidence: 99%

Chaos-assisted instanton tunneling in one-dimensional perturbed periodic potential

Kuvshinov

Kuzmin²,

Shulyakovsky³

2003

Phys. Rev. E

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“…7) No doubt that some classical motivations which brought us to the formulation of the chaos criterion had to be used. Further justification of the proposed criterion and the check of its correspondence with the notion of classical chaos are to be done.…”

Section: )mentioning

confidence: 99%

“…We consider proposed by us chaos criterion for quantum fields 7) in the context of existing results obtained in this direction. Also we discuss possible manifestations of deterministic chaos in quantum field theory.…”

Section: §1 Introductionmentioning

confidence: 99%

Deterministic Chaos in Quantum Field Theory

Kuvshinov¹,

Kuzmin²

2003

Prog. Theor. Phys. Suppl.

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We discuss the necessity and demonstrate the validity of introduction the notion of deterministic chaos in quantum field theory. Brief review of the existing approaches to this problem is given. We compare proposed chaos criterion for quantum fields with existing ones. Its consequences in particle physics are also discussed. §1. IntroductionChaos phenomenon attracts much attention in various fields of natural sciences, from celestial mechanics 1) ( pp.349-359) and behavior of social systems 2) to quantum mechanics 3) and atomic physics. 4) Though the understanding of the reasons and regimes of chaotic behavior in classical (Hamiltonian) systems is already achieved in main, 5) problems connected with properties, manifestations and even definition of deterministic chaos in quantum world are still basically open. 6), 7) Prevalence of chaotic motions in the majority of natural phenomena explains the fundamental and applied significance of its study. Particulary, chaotic behavior is intrinsical to classical gauge fields in modern theories of particle interactions 8), 9), 10) as well it plays crucial role for quantum tunneling control, which is of practical importance. 11)In this paper we discuss chaos phenomenon in the context of quantum field theory (QFT). We premise the consideration of our main topic by some motivations. Investigation of the classical gauge field dynamics from the viewpoint of chaos was started in a few years after recognition of gauge theories based on SU (3) and SU (2) ⊗ U (1) groups as theories of strong and electroweak interactions respectively. Nonabelian gauge fields form complicated nonlinear system with large number of degrees of freedom, which behavior demonstrates a lot of regimes when parameters vary. Besides the investigation of classical gauge fields to be interesting from the viewpoint of nonlinear dynamics, it is also important from the viewpoint of particle physics (particulary QCD), where large progress is achieved in understanding of perturbative phenomena, but comparatively little is known about the non-perturbative evolution of quarks and gluons. Namely, the confinement phenomenon responsible for absence of free colored objects is waiting for its explanation (however a lot of results is obtained in this direction, for review see Ref. 12) ). The problem is that there are no exact methods for description of non-perturbative evolution of quantum fields, when coupling between them is not too small (there is no small parameter) and perturbative expansions can not be applied. The first step for understanding of quantum dynamics in this coupling regime is the investigation of the classical behavtypeset using PTPT E X.cls Ver.0.89

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“…Using well known technique based on Toda criterion of local instability [20,15] one can obtain that there is an order to chaos transition with the rise of the density of energy of the system. Critical density of energy (minus vacuum density of energy which is non-zero) is given by the following relation…”

confidence: 99%

“…There are papers devoted to chaos in quantum field theory [4,15]. Nevertheless there is no generally recognized definition of chaos for quantum systems in QM (beyond semiclassical approximation) and QFT [7].…”

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The Influence of Quantum Field Fluctuations on Chaotic Dynamics of YangMills System

Kuvshinov¹,

Kuzmin²

2002

JNMP

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On example of the model field system we demonstrate that quantum fluctuations of non-abelian gauge fields leading to radiative corrections to Higgs potential and spontaneous symmetry breaking can generate order region in phase space of inherently chaotic classical field system. We demonstrate on the example of another model field system that quantum fluctuations do not influence on the chaotic dynamics of nonabelian Yang-Mills fields if the ratio of bare coupling constants of Yang-Mills and Higgs fields is larger then some critical value. This critical value is estimated.

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Towards chaos criterion in quantum field theory

Cited by 13 publications

References 12 publications

Chaos-assisted instanton tunneling in one-dimensional perturbed periodic potential

Chaos-assisted instanton tunneling in one-dimensional perturbed periodic potential

Deterministic Chaos in Quantum Field Theory

The Influence of Quantum Field Fluctuations on Chaotic Dynamics of YangMills System

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Towards chaos criterion in quantum field theory

Cited by 13 publications

References 12 publications

Chaos-assisted instanton tunneling in one-dimensional perturbed periodic potential

Chaos-assisted instanton tunneling in one-dimensional perturbed periodic potential

Deterministic Chaos in Quantum Field Theory

The Influence of Quantum Field Fluctuations on Chaotic Dynamics of Yang­Mills System

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The Influence of Quantum Field Fluctuations on Chaotic Dynamics of YangMills System